I Simultaneity: Train and Lightning Thought Experiment

In this experiment, a man is standing on a train platform. A woman is sitted in the middle of a moving train travelling towards the man. When the train is half past the man, lightning strikes at the same instant at both ends of the train. The man sees the lightning at the same time. This makes sense since the distance travelled by light from both ends is the same.

However, the thought experiment propose that the woman sees the light from the front of the train first. This is because she 'runs' into light from the front since she is moving forward with the train.She then conclude that lightning struck the front first since she is equidistant from the front and back of the train.

I am confused. Since the train is not accelerating, it can be treated as an inertial frame of reference. Speed of light c should be constant in the woman's frame of reference. Thus when only regarding the woman's frame, shdn't she see both lightning at the same time? Since both light travels at c and have to cover half of the train's length.

The fact that the woman runs into the front lightning is the observation from the man's frame of reference. So when we are talking about the woman's observations, why are we trying to use the man's frame of reference to predict the results? Shdn't we be isolating the woman's frame of reference and analysing that independently?

I hope my words are clear! Thanks for reading and help me out if you can

Thus when only regarding the woman's frame, shdn't she see both lightning at the same time? Since both light travels at c and have to cover half of the train's length.

No, this is the entire point. The strikes are simultaneous in the man's frame by definition. If you postulate that the strikes are simultaneous in the woman's frame it is a different setup and so in this setup you cannot get rid of the man's frame because it is part of the definition of when the lighting strike. The entire point is to compare what happen in the two frames and the conclusion is that if the strikes are simultaneous in the man's frame, they are not in the woman's.

Seen from the man's frame:

He observes the strikes at the same time because they are equidistant from him and occur at the same time.

The woman observes the strikes at different times because they are equidistant but the woman is moving towards one of the signals.

We can conclude the following about the woman's frame (she has to observe the same things as the man, i.e., that the man sees the strikes at the same time and she does not):

The flashes are occur at the same distance from her because they occur at the ends of the train and she is in the middle.

She sees one flash before the other, since the speed of light is the same in all directions, the one she sees first must have occurred first. Hence the strikes were not simultaneous. One occurred before she passed the man and the other after.

Even if the strikes did not occur at the same time, the man is moving away from the one that occurred first and it will therefore take the light from that strike longer to catch up with him - resulting in that he sees both strikes at the same time.

I am confused. Since the train is not accelerating, it can be treated as an inertial frame of reference. Speed of light c should be constant in the woman's frame of reference.

Exactly, but your conclusion is not the logical one. The logical conclusion is that the strikes are not simultaneous in her frame. Otherwise the descriptions from the different inertial frames would not follow the same rules.

Thus when only regarding the woman's frame, shdn't she see both lightning at the same time? Since both light travels at c and have to cover half of the train's length.

This would be true only if the strikes were simultaneous in her frame. Your conclusion from this should be that, since whether she sees one first or both at the same time cannot depend on the inertial frame, you have to drop the assumption that the strikes were simultaneous in her frame.

The fact that the woman runs into the front lightning is the observation from the man's frame of reference. So when we are talking about the woman's observations, why are we trying to use the man's frame of reference to predict the results? Shdn't we be isolating the woman's frame of reference and analysing that independently?

Which signal arrives to the woman first cannot be frame dependent since any frame has to describe the same physical reality. You can do the computation in whatever frame you would like and you should get the same result.

Which signal arrives to the woman first cannot be frame dependent since any frame has to describe the same physical reality.

What qualifies as physical reality? Couldn't one say that to the man it's physical reality that flashes of light hit the front and back of the train at the same time? The distinction maybe needs to be made between spatially separated events and events that occur at the same location.

taneyfan: Suppose there is a device sitting next to the woman, with forward and backward looking sensors, that emits a beep when light strikes both sensors at the same time (in its frame of reference). If we analyze the situation in the man's frame of reference, he concludes that there should be no beep. Now it would be a strange world if the man didn't hear a beep but the woman did because she was moving relative to him. So she concludes that the light flashes reach her at different times. Since the lengths of the train in front and behind her are the same and the speed of light is c in both directions, the time taken for the flashes to reach her has to be the same, and she concludes that one occurred earlier than the other. Note that we're considering the simultaneity of two events at a given location in the woman's frame, that of the device.

In this experiment, a man is standing on a train platform. A woman is sitted in the middle of a moving train travelling towards the man. When the train is half past the man, lightning strikes at the same instant at both ends of the train. The man sees the lightning at the same time. This makes sense since the distance travelled by light from both ends is the same.

However, the thought experiment propose that the woman sees the light from the front of the train first. This is because she 'runs' into light from the front since she is moving forward with the train.She then conclude that lightning struck the front first since she is equidistant from the front and back of the train.

I am confused. Since the train is not accelerating, it can be treated as an inertial frame of reference. Speed of light c should be constant in the woman's frame of reference. Thus when only regarding the woman's frame, shdn't she see both lightning at the same time? Since both light travels at c and have to cover half of the train's length.

Consider this: What is the woman's position with respect to the tracks when she sees each strike? If you are watching this from the tracks, it is clear that she is at a different point along the tracks when the light from each strike reaches her. Now consider this from the view of the woman. If, as you suggest, she sees the strikes simultaneously then she will be at a single point along the tracks when she sees both strikes. This would set up a physical contradiction between what shes says happens and what the person standing along the tracks says happened. For example, give her a camera and have her take a picture of the tracks when shes sees the strikes. Give a camera to each of a string of observers placed along the tracks with the instructions to take a picture of her is she is next to them when the light reaches her. After the experiment is over, we bring the photos together and compare them. You can't have her showing up with just one photo while the track cameras recorded two photos of her taking a picture, each at a different point of the tracks.
Once you agree that both observers must agree that the woman sees the strikes at different times and at different times, then you apply the constant speed of light and her equal distance from the ends of the train to determine that the strikes did not happen simultaneously according to her.

The fact that the woman runs into the front lightning is the observation from the man's frame of reference. So when we are talking about the woman's observations, why are we trying to use the man's frame of reference to predict the results? Shdn't we be isolating the woman's frame of reference and analysing that independently?

The point is that if she meets the light from the strikes at different times and different points of the tracks in one frame (the man's) she has to meet them at different times and different points of the tracks in her frame. We start in the man's frame simply because we set hings up so that it would be the frame in which the strikes occurred simultaneously. We then use this frame to worked out the events that both frames must agree on (for instance, both frames must agree that the light from the flashes reach the man simultaneously), to work out the sequence of events in the Woman's frame. You can't completely isolate the woman's frame from the man's frames because there are common events that they both must agree on.

The physical reality is four dimensional. The emissions happen at different events. There is more than one way to slice spacetime into sets of "all of space, now". Different ways of doing that lead to different ideas about what's simultaneous. That's the thing that isn't physical - it's just a matter of which slicing ("foliation") is convenient for you.

By this I mean any measurable frame independent statement, which simultaneity is not (unless you in the statement specify the frame in which the events are simultaneous).

I guess the issue for me is that Einstein's train thought experiment is used to derive the fact that simultaneity is relative (presumably before knowing the Lorentz transformation, from which all of this simultaneity stuff can be easily derived). So can we make any statements about simultaneity being frame independent or not during the analysis of the experiment?

I guess the issue for me is that Einstein's train thought experiment is used to derive the fact that simultaneity is relative (presumably before knowing the Lorentz transformation, from which all of this simultaneity stuff can be easily derived). So can we make any statements about simultaneity being frame independent or not during the analysis of the experiment?

The statement is about events along the world lines of the observers. This is well defined.

For the man the two flashes arrive at the same time. This is an example of a physical reality. It's a single event because it occurs at a single location at a single time. You might imagine, for example, that the man's head will explode if the two flashes arrive at the same time. The woman will agree that the two flashes arrived at the same time and that therefore the man's head explodes. It's a physical reality. It can't be that the head explodes in one frame and not in the other.

Likewise they'll both agree that the woman's head doesn't explode because the flashes don't hit her at the same time.

But the thought experiment is designed to show that a pair of spatially separated events can be simultaneous in one frame and not in another.

I guess the issue for me is that Einstein's train thought experiment is used to derive the fact that simultaneity is relative (presumably before knowing the Lorentz transformation, from which all of this simultaneity stuff can be easily derived).

It all follows from the two postulates. You can use the two postulates to derive the Lorentz transformation equations, which can then in turn be used to illustrate that simultaneity is relative. Or you can use the two postulates to illustrate it directly (by using, for example, the train thought experiment).

To borrow an example from the literature, suppose you have a small tape player that starts when a light signal hits the front side and stops when it hits the back side. The tape player is small enough that the internal propagation delays are negligible - an important point. If simultaneity were frame dependent, the tape player could play in some frames, and not play in others. But this doesn't make sense - everyone agrees on whether the tape player plays, or does not play, regardless of their frame of reference.

Sometimes the tape player is replaced more dramatically with a bomb.

It's important that the tape player be small enough to be regarded as point-like, but this shouldn't be a huge issue in practice. For instance, you could imagine the train cars being 100km long, and the tape player being a 1 cm.

To borrow an example from the literature, suppose you have a small tape player that starts when a light signal hits the front side and stops when it hits the back side. The tape player is small enough that the internal propagation delays are negligible - an important point.

If simultaneity were frame dependent, the tape player could play in some frames, and not play in others.

But the frame dependence of simultaneity is the whole point of the train experiment. Again, I think the key point is distinguishing between spatially separated events and events at the same location such as your tape player example.

You might imagine, for example, that the man's head will explode if the two flashes arrive at the same time. The woman will agree that the two flashes arrived at the same time and that therefore the man's head explodes. It's a physical reality. It can't be that the head explodes in one frame and not in the other.

But the frame dependence of simultaneity is the whole point of the train experiment. Again, I think the key point is distinguishing between spatially separated events and events at the same location such as your tape player example.

Not just events at the same location, but events at the same location and at the same time! We then call it a single event. If it happens according to one observer, it happens according all observers.

The relativity of simultaneity does indeed to refer to spatially separated events. But there's more to the story. For the two spatially separated events to occur simultaneously in one frame of reference, they have to be spatially separated in all frames of reference. No observer can be present at both events because it would require him to travel at a speed that's faster than light. Thus the order in which the events occur depends on the observer's velocity. The events are said to be causally disconnected, or in other words, they have a spacelike (as opposed to timelike) separation.

In this experiment, a man is standing on a train platform. A woman is sitted in the middle of a moving train travelling towards the man. When the train is half past the man, lightning strikes at the same instant at both ends of the train. The man sees the lightning at the same time. This makes sense since the distance travelled by light from both ends is the same.

However, the thought experiment propose that the woman sees the light from the front of the train first. This is because she 'runs' into light from the front since she is moving forward with the train.She then conclude that lightning struck the front first since she is equidistant from the front and back of the train.

I am confused. Since the train is not accelerating, it can be treated as an inertial frame of reference. Speed of light c should be constant in the woman's frame of reference. Thus when only regarding the woman's frame, shdn't she see both lightning at the same time? [..]]

Physical reality doesn't need to "qualify". It exists by itself and wends its way through things in an order which -- as physics is currently understood -- is unknowable. If event A is capable of causing event B, then it's impossible to see event B before event A. Otherwise it's a toss-up, and causality ensures that it doesn't make any difference.

On a classical scale, there are three kinds of direction:
Time-like, with both orientation and magnitude.
Light-like, with orientation but not magnitude.
Space-like, with magnitude but not orientation.
Event A can cause event B if and only if there is a path of time-like or light-like segments oriented from A to B.

Staff: Mentor

On a classical scale, there are three kinds of direction:
Time-like, with both orientation and magnitude.
Light-like, with orientation but not magnitude.
Space-like, with magnitude but not orientation.

This is not correct. Where are you getting this from?

The correct statement is that all three types of tangent vectors (the proper way of saying "direction") have an orientation; timelike vectors have negative squared magnitude (using the -+++ metric signature convention), lightlike vectors have zero squared magnitude, and spacelike vectors have positive squared magnitude.

I was referring to line segments, not vectors. Yes of course you can orient a line segment through space by putting an arrow at one end. But if the line segment is time-like or light-like it has an orientation even without an arrow, because one end is later than the other.

Staff: Mentor

I see. This works OK in flat spacetime, but in curved spacetime (i.e., in the presence of gravity), it has limitations. The tangent vector approach avoids these limitations.

However, there is also an alternative, which is to focus, not on the line segment itself, but on the two endpoints, i.e., on a pair of events. The separation of these events, timelike, lightlike, or spacelike, is an invariant even in curved spacetime and doesn't bring in any of the limitations of the "line segment" view.

if the line segment is time-like or light-like it has an orientation even without an arrow, because one end is later than the other.

Ah, I see, by "orientation" you mean "time ordering". Yes, this is true, two events which are timelike or lightlike separated have an invariant time ordering, whereas two spacelike separated events do not. However, "orientation" is not a good term for this, because it has other meanings: the one I had assumed before, which is more or less the "direction in spacetime" that a vector points (and as noted, all three types of vectors have orientations in this sense), and also the parity or "handedness" of a set of basis vectors.

Consider Einstein's Train example.
You have a train with an observer at the midpoint between the ends. you also have an observer standing along the tracks. Lightning strikes the end of the trains when, according to the track-side observer the train observer is passing him. Thus he sees the light from the strikes at the same time and determines that the strikes occurred simultaneously. Thus, according to the frame of the tracks, events look like this:..

There is still more. See his full explanation in the post.

These are the simulations that helped my SR learning.
With courtesy of @Janus